Short answer: It depends on the organization.
Long Answer: Without polling tons of companies, it's hard to quantify how often QA teams get involved with writing tests that involve mock objects. In my experience, most small-to-medium software development companies tend to lean on their developers to write unit, integration, and UI tests. The QA departments in such firms usually test new features and enhancements as well as whether defects were fixed (ideally, your tests are doing this, but in practice, not every developer writes a test to check against the defect they just fixed).
Many larger companies will employ QA teams with programming experience. Such teams are known to write UI tests (such as Selenium for browser applications) as such tests don't require knowledge of the code to check functionality; UI tests typically check expected UI responses versus actual responses.
In some cases, the QA team will contribute to writing unit and integration tests as well, although in my experience it's rare to see QA being completely responsible for such tests. Typically-speaking, it's going to be easier for the developers to write tests. That said, a QA team member who illustrates understanding of the code and ability to write unit and integration tests (including utilization of mock objects for such tests) would quickly become a leader in such a department.
Recommendation: You should focus on learning good UI design and practices, testing for common and boundary cases, and obtaining an understanding about user experiences and expectations in general as a basis for your QA career. However, learning about the development side of QA (i.e. writing tests with and without mock objects) will definitely help your career. If you have the time, learn it.